Hello again jeremit,
Most of your work is absolutely correct. I've spotted a small mistake
in your graph for question 2, though.
Question 1
I don't think this can be put any simpler than you did. The height of
the cork above the sea floor as a function of time can certainly be
described by a sinusoidal function, just as you did. Let's say, for
example, that if the sea were calm, the cork would be 100 ft above the
sea floor. A plausible function for the height of the cork could then
be:
Height(t) = sin(t) + 100
The question in the image you supplied asks about the vertical
velocity of the cork rather than its height. Now, this velocity is
simply the derivative of the height with respect to time. Following
the example above, this yields:
d(Height)/dt = cos(t)
Since cosine is still a sinusoidal function, it's correct to graph the
velocity as you did in your graph. Notice that it's important that
this function crosses the x-axis (i.e. takes on negative values, as
the cork moves both up and down), while the height function does not
(as it's not possible for the cork to go below the sea floor)
Question 2
The graphs for inflow and outflow you provided are plausible except
for the fact that the level of the reservoir doesn't appear to be
equal in Jan 1993 and Jan 1994. How can you tell? Basically, in order
for the quantity of water to be equal in Jan 1993 and Jan 1994, we
should have the TOTAL INFLOW of water during 1993 is equal to the
TOTAL OUTFLOW. Now, the inflow and outflow graphs show the *rate* at
which the water goes in and out of the reservoir. Therefore, TOTAL
inflow and outflow are represented by the *areas* under each curve (in
other words, we must take the integral of the inflow and outflow rates
in order to get the inflow and outflow levels). We conclude that, in
order for the quantity of water to be equal in Jan 1993 and Jan 1994,
the area under each curve should be equal throughout 1993. In the
graph you supplied, however, it appears that the outflow is larger
than the inflow. You can seev this in the following colored graph,
based on yours:
http://img60.imageshack.us/img60/763/calcshit001boj9np1.jpg
As you can see, the red area (total outflow) appears to be greater
than the blue area (total inflow). Therefore, the quantity of water
would be smaller in January 1994 than in January 1993. A correct
version could something like this:
http://img109.imageshack.us/img109/6004/inflowoutflowpw8.gif
Notice that the area under both curves from Jan 1993 through Jan 1994
is roughly equal, implying that the quantity of water that went into
the reservoir is approximately the same as the quantity that went out
of it. Therefore, the quantity of water in the reservoir is roughly
the same in Jan 1993 and in Jan 1994.
Another feature of this graph is that the inflow is roughly cyclical,
with a length of one year. This could make sense, given that the
rainfall, which could be the only source of water for the reservoir,
follows a cyclical pattern (more rain at certain times of the year and
less rain at others). Finally, the outflow is lower in 1994. This can
be rationalized by assuming the authorities are saving water for some
purpose. It's clear from the graph that the quantity of water by
mid-1994 is much higher than in Jan 1994.
Question 3
You got these two 100% right. Great job!
I hope this helps! If you have any doubt regarding my answer, please
don't hesitate to request clarification before rating it. Otherwise, I
await your rating and final comments.
Best wishes!
elmarto |